Check your Pizza Cutting Habits

Before Christ­mas, I asked my Pre alge­bra stu­dents why we cut our pies and piz­zas into 8 slices. While there is the occa­sion­al rebel slic­ing the pies into 6 slices and some piz­zas into 12 slices, the vast major­i­ty of us seem to favor 8. Is it because we all love the num­ber 8? What’s going on here? For the most part, they still haven’t told me. 

This sort of slic­ing pref­er­ence is a clas­sic exam­ple of some­thing we do, yet with­out real­iz­ing the math behind the intu­ition to make our lives eas­i­er. It’s so obvi­ous to us that we fail to see. Let’s take a clos­er look. Imag­ine cut­ting a piz­za — where do you make the first cut? Why do you make the cut there? 

Now I know that some of you, most like­ly the rebels among you, may refuse to see what’s nat­ur­al and insist on mak­ing your first piz­za cut on the edge. This pat­tern results in var­i­ous sized strips of piz­za with vary­ing amounts of crust to piz­za ratio. It’s prac­ti­cal­ly chaos. Let’s remem­ber that we are ana­lyz­ing a nat­ur­al non rebel­lious habit — our first cut on a piz­za is cut­ting it in half. 

In fact, every cut that we make on a piz­za cuts the piz­za in half. Even when we are slic­ing the piz­za into 6 or 12 slices. How­ev­er, there is some­thing about cut­ting until we have 8 sym­met­ri­cal slices that brings this to the next lev­el. Can you fig­ure it out?